Help Me Please?

Question

lim( x^3+x^2)^1/2 sin3.14/x=0
x>0

Answer 1

I'm not sure what your asking here. is that sin(pi/x) or sin(pi)/x so I don't know the answer. But you can probably figure it out first by factoring (x^3 + x^2)^1/2 as

(x^3 + x^2)^1/2 = (x^2*(x+1))^1/2 = (x^2)^1/2*(x+1)^1/2

but (x^2)^1/2 = x so this becomes x*(x+1)^1/2. Then try cancelling terms that become infinite as x->0

Answer 2

lim( x^3+x^2)^1/2 sin3.14/x=0
x>0 I assume you meant:
lim( x^3+x^2)^1/2 sin3.14/x
x>0
This limit takes the form of 0^ (undefined) and so has no limit.
As x --> 0 from the left f(x) --> infinity.
As x --> 0 from the right x --> infinity

Answer 3

Makes no sense. You can take the limit of an expression, but not an equation.

Answer 4

What's the question? Are you asking how to show that this limit does go to zero?